Guaranteed performance state estimation of static neural networks with time-varying delay

This paper is concerned with studying two kinds of guaranteed performance state estimation problems for static neural networks with time-varying delay. Both delay-independent and delay-dependent design criteria are presented under which the resulting estimation error system is globally asymptotically stable and a prescribed performance is guaranteed in the H_∞ or generalized H₂ sense. It is shown that the gain matrices of the state estimator and the optimal performance indexes can be simultaneously obtained by solving convex optimization problems subject to linear matrix inequalities. It is worth noting that no slack variable is introduced in the proposed conditions, and thus the computational burden is reduced. The effectiveness of the developed results is finally demonstrated by simulation examples.     

State estimation for discrete-time neural networks with time-varying delay

This article deals with the problem of delay-dependent state estimation for discrete-time neural networks with time-varying delay. Our objective is to design a state estimator for the neuron states through available output measurements such that the error state system is guaranteed to be globally exponentially stable. Based on the linear matrix inequality approach, a delay-dependent condition is developed for the existence of the desired state estimator via a novel Lyapunov functional. The obtained condition has less conservativeness than the existing ones, which is demonstrated by a numerical example.     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Stability analysis for recurrent neural networks with time-varying delay

This paper is concerned with the stability analysis for static recurrent neural networks （RNNs） with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities （LMIs）, the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.     

A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices

A new kind of recurrent neural network is presented for solving the Lyapunov equation with time-varying coefficient matrices. Different from other neural-computation approaches, the neural network is developed by following Zhang et al.'s design method, which is capable of solving the time-varying Lyapunov equation. The resultant Zhang neural network (ZNN) with implicit dynamics could globally exponentially converge to the exact time-varying solution of such a Lyapunov equation. Computer-simulation results substantiate that the proposed recurrent neural network could achieve much superior performance on solving the Lyapunov equation with time-varying coefficient matrices, as compared to conventional gradient-based neural networks (GNN).     

Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.     

New stability criteria for recurrent neural networks with a time-varying delay

This paper deals with the stability of static recurrent neural networks (RNNs) with a time-varying delay. An augmented Lyapunov-Krasovskii functional is employed, in which some useful terms are included. Furthermore, the relationship among the timevarying delay, its upper bound and their difierence, is taken into account, and novel bounding techniques for 1- τ(t) are employed. As a result, without ignoring any useful term in the derivative of the Lyapunov-Krasovskii functional, the resulting delay-dependent criteria show less conservative than the existing ones. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.     

Improved results on state estimation for neural networks with time-varying delays

In this paper, some improved results on the state estimation problem for recurrent neural networks with both time-varying and distributed time-varying delays are presented. Through available output measurements, an improved delay-dependent criterion is established to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable, and the derivative of time-delay being less than 1 is removed, which generalize the existent methods. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed results.     

An estimation of the domain of attraction for recurrent neural networks with time-varying delays

Based on Lyapunov–Krasovskii functional or Lyapunov–Razumikhin functional method and invariant set principle, we presented a new method to estimate the domain of attraction for general recurrent neural networks with time-varying delays. Convex optimization method is proposed to enlarge and estimate the domain of attraction. Local exponential stability conditions are derived, which can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can be easily checked in both analysis and design.     

New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay

This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results. Supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z183), China Postdoctoral Sciencer Foundation (Grant No. 20080431150), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801451096)     

State estimation of recurrent neural networks with interval time-varying delay: an improved delay-dependent approach

This paper is concerned with the state estimation problem for a class of recurrent neural networks with interval time-varying delay, where time delay includes either slow or fast time-varying delay. A novel delay-dependent criterion, in which the rate–range of time delay is also considered, is established to estimate the neuron states through available output measurements such that, for all admissible time delays, the dynamics of the estimation error system is globally asymptotically stable. The proposed method is based on a new Lyapunov–Krasovskii functional with triple-integral terms and free-weighting matrix approach. Numerical examples are given to illustrate the effectiveness of the method.     

A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay

This paper is concerned with delay-dependent passivity analysis for interval neural networks with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new passivity criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness of the developed techniques.     

State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results.     

Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay

In this article, based on Lyapunov–Krasovskii functional approach and improved delay-partitioning idea, a new sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic time-varying delay is addressed. Together with general convex combination method, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time delay range and its derivative, which has wider application fields than those present ones. It can be shown by the numerical examples that our method reduces the conservatism much more effectively than earlier reported ones. Especially, the conservatism can be further decreased by thinning the delay intervals.     

Some improved methods to analysis stability of recurrent neural networks with interval time-varying delays

This paper considers the delay-dependent stability problem of recurrent neural networks with interval time-varying delays. An appropriate Lyapunov–Krasovskii functional is constructed and the combination method of Wirtinger inequality and reciprocally convex optimization technique is employed. Combing a new activation function segmentation method of the boundary condition and the orthogonal complement lemma, three further improved delay-dependent stability criteria are established. Finally, two numerical examples show the effectiveness of our proposed method by comparison with the recent existing works.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Ultimate boundedness of stochastic Hopfield neural networks with time-varying delays

By employing Lyapunov functional theory as well as linear matrix inequalities, ultimate boundedness of stochastic Hopfield neural networks (HNN) with time-varying delays is investigated. Sufficient criteria on ultimate boundedness of stochastic HNN are firstly obtained, which fills up a gap and includes deterministic systems as our special case. Finally, numerical simulations are presented to illustrate the correctness and effectiveness of our theoretical results.     

Impulses-induced exponential stability in recurrent delayed neural networks

The present paper formulates and studies a model of recurrent neural networks with time-varying delays in the presence of impulsive connectivity among the neurons. This model can well describe practical architectures of more realistic neural networks. Some novel yet generic criteria for global exponential stability of such neural networks are derived by establishing an extended Halanay differential inequality on impulsive delayed dynamical systems. The distinctive feature of this work is to address exponential stability issues without a priori stability assumption for the corresponding delayed neural networks without impulses. It is shown that the impulses in neuronal connectivity play an important role in inducing global exponential stability of recurrent delayed neural networks even if it may be unstable or chaotic itself. Furthermore, example and simulation are given to illustrate the practical nature of the novel results.     

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.     

Delay dependent stability criteria for recurrent neural networks with time varying delays

This paper aims to present some delay-dependent global asymptotic stability criteria for recurrent neural networks with time varying delays. The obtained results have no restriction on the magnitude of derivative of time varying delay, and can be easily checked due to the form of linear matrix inequality. By comparison with some previous results, the obtained results are less conservative. A numerical example is utilized to demonstrate the effectiveness of the obtained results.